Question

Mass of an imaginary planet is double earth's mass and radius is 1.5 times earth's radius. Using mass and radius, calculate the acceleration of gravity for the imaginary planet.
Using the pendulum formula for the period of oscillation, and your new
acceleration of gravity, determine the period of a pendulum that is 1 meter long
and it is on this planet.
which sport would be easier to do
on this planet, if any, and explain the advantages or disadvantages of the new
acceleration of gravity.

Answer 1

Step 1 — gravity on the imaginary planet
g scales as GM/R^2. If M' = 2Me and R' = 1.5Re then
g' = G·(2Me)/(1.5Re)^2 = (2/2.25)·g = 0.888888...·g.

Using g = 9.81 m/s^2:
g' = 9.81 × (2/2.25) ≈ 8.72 m/s^2.
(So weight would be ≈11.1% less than on Earth.)

Step 2 — period of a 1 m pendulum
T = 2π √(L/g). For L = 1 m and g' = 8.72 m/s^2:
T' = 2π √(1/8.72) ≈ 2.13 s.

For comparison, on Earth T ≈ 2.01 s, so the period on the new planet is about 5.9% longer.

Step 3 — which sports would be easier and why
- Easier: jumping and throwing sports (high jump, long jump, basketball, volleyball, diving, some gymnastics elements). Because g is ~11% smaller, for the same takeoff force an athlete will reach slightly higher and stay in the air longer (hang time increases ≈ 5.9%), and projectile ranges (kicks/throws) increase ≈ 12.5% for the same launch speeds.
- Also easier: lifting static weights is easier by ~11% because the weight (mg) is smaller, though the mass (inertia) is unchanged.
- Disadvantages / caveats:
- Inertia is the same: objects still resist horizontal acceleration the same way, so controlling moving masses is unchanged.
- Lower normal force reduces maximum friction (friction ∝ normal force). That can reduce how much horizontal push an athlete can get from the ground, possibly affecting sprint starts and rapid direction changes. The net effect on sprinting/sudden accelerations is complex and depends on whether athletes are friction-limited.
- Ball bounces, dribbles and equipment behavior change (longer trajectories, different bounce heights), so skill timing must adapt.
- Balance and coordination may be affected until people adapt to the different gravity.

Bottom line: a modestly lower gravity (≈8.72 m/s^2) would particularly favor jumping and throwing events, give slightly longer pendulum periods (≈2.13 s for a 1 m pendulum), and produce modest but noticeable changes in many sports.